Summary: ALTERNATIVE INTEGRAL EQUATIONS FOR THE
ITERATIVE SOLUTION OF ACOUSTIC SCATTERING
PROBLEMS
by X. ANTOINE
(Math´ematiques pour l'Industrie et la Physique, MIP UMR-5640, UFR MIG, Universit´e Paul
Sabatier, 118 route de Narbonne, 31062 Toulouse cedex, France)
and M. DARBAS
(D´epartement de G´enie Math´ematique, INSA, MIP UMR-5640, Complexe Scientifique de
Rangueil, 31077, Toulouse cedex 4, France)
[Received 15 March 2003. Revises 3 November 2003 and 26 April 2004]
Summary
This paper addresses the first step of the derivation of well-conditioned integral formulations for
the iterative solution of exterior acoustic boundary-value problems. These new formulations are
designed to be implemented in a fast multipole method coupled to a Krylov subspace iterative
algorithm. Their construction is based on the on-surface radiation condition formalism. Both
theoretical developments and numerical aspects are examined in detail. This approach can be
viewed as a generalization of the usual Burton­Miller integral equations.
1. Introduction
A very popular method for solving the acoustic scattering problem of a time-harmonic wave in an
unbounded domain is provided by the integral equation method (1 to 3). Even if other efficient